Abstract

It is shown that the decay character of the phononspectrum in superfluidhelium is a consequence of the analyticity and parity of the boson self-energy as a function of energy and momentum. Previous self-consistent numerical calculations have shown that because of the strong interaction between the particles in Bose-Einstein condensate the normal and anomalous boson self-energies are analytical functions of the momentum and energy and on the mass shell, in the long-wavelength limit, they depend only on the squared momentum. It is shown on this basis that the phononspectrum of a bose liquid is a decay spectrum in complete agreement with the experimental data on neutron scattering and the interaction of the high- and low-frequency phonons in superfluidhelium.

We thank I. N. Adamenko for providing complete information on the experimental and theoretical studies of the features of the decay phonon spectrum in He II. One of us (É. A. P.) thanks the Ukrainian National Center for Technology for partial financial support of this work (Project No. 3718).